Final answer:
A conjunction with a tautology is always true, so the answer to the student's question is 'a. True'. A hypothesis is similar to a 'suggestion'. A disjunctive syllogism's validity follows from the truth of its premises.
Step-by-step explanation:
Conjunction and Tautology
A conjunction that has a tautology as one of its conjuncts is always true. This is because a tautology is a statement that is true in all possible circumstances. By definition, a tautology will never make the conjunction false no matter what the other conjunct is. For example, if we have "X and Y" where X is a tautology, the truth of Y is irrelevant; X will always ensure the conjunction is true.
Therefore, the answer to the student's question would be:
a. True
When it comes to a hypothesis, the word closest in meaning would be d. suggestion, because a hypothesis is a proposed explanation made on the basis of limited evidence as a starting point for further investigation.
Lastly, understanding the validity of deductive inferences, such as in a disjunctive syllogism, is critical in mathematics. A disjunctive syllogism is valid because if one of the premises is true, the conclusion must follow.